So I'm building an HTPC for myself, it's going to be outputting at 1080p to my television, running local media but also maybe streaming over the network. It'll also have a ton of storage as I'm going to use it as a network backup solution for my desktop PC.

How CPU intensive is this? I was just going to buy a cheap 3 core athlon to keep costs down but if I should be stepping up to a quad core / chip with more cache to get this done I will. I figure the biggest "load" would be decoding HD video, but I'm still not sure if that's actually intensive.

AFAIK, a decent dual core is all you really need. Have a read through Anandtech's aritcles on Ivy Bridge IGP for HTPC and AMD Trinity for HTPC. Something like an AMD A6-5400K for $75 and a 65W TDP might be just what the doctor ordered. Takes care of your CPU and GPU. I plan on upgrading my HTPC with one of those over the holidays.

Note: I am *not* recommending the solution below, I'm just putting it out there for context.

I have a 2008 Core 2 Duo notebook with crappy x4500 chipset graphics. However, the notebook does have HDMI output. I'm a big Linux guy, so I have gotten 1080P video output from the notebook to my HD-TV on a KDE 4 desktop including audio channeled over the HDMI, and the video plays just fine (I recommend VLC or a fancy media-centric Linux distro like XBMC).

Now obviously video playback is not the only thing that people do with HTPCs, but you really don't need to have a huge CPU or GPU to do the basics. If you want to really use this HTPC for games, then you need to look into better GPU solutions, but practically any modern system can do the basic stuff just fine. The fancier points come into price/performance ratios and having a quiet system.